Related papers: Quantifying operator spreading and chaos in Krylov…
We investigate the operator growth dynamics of the transverse field Ising spin chain in one dimension as varying the strength of the longitudinal field. An operator in the Heisenberg picture spreads in the extended Hilbert space. Recently,…
In this work, we investigate the quantum chaos in various $T\bar{T}$-deformed SYK models with finite $N$, including the SYK$_4$, the supersymmetric SYK$_4$, and the SYK$_2$ models. We numerically study the evolution of the spectral form…
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and…
Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are prerogative of quantum chaotic systems and how they relate to more standard…
In this work, we find that the complexity of quantum many-body states, defined as a spread in the Krylov basis, may serve as a new probe that distinguishes topological phases of matter. We illustrate this analytically in one of the…
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…
Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…
More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…
Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a…
We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…
Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…
Heisenberg time evolution under a chaotic many-body Hamiltonian $H$ transforms an initially simple operator into an increasingly complex one, as it spreads over Hilbert space. Krylov complexity, or `K-complexity', quantifies this growth…
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum…
We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…
Dynamical properties of classical chaotic systems, for instance relaxation, can be understood as emerging from the time evolution of initially smooth long-wavelength densities to ever finer short-wavelength densities with fractal structure.…
Multipartite entanglement is a crucial resource for advancing quantum technologies, with considerable research efforts directed toward achieving its rapid and scalable generation. In this work, we derive an analytical expression for the…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
We introduce and review a new complexity measure, called `Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics, serving as a canonical measure of operator growth and spreading. Krylov complexity, underpinned…
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution…